Problem: Which of the following numbers is a factor of 182? ${6,9,10,11,13}$
Explanation: By definition, a factor of a number will divide evenly into that number. We can start by dividing $182$ by each of our answer choices. $182 \div 6 = 30\text{ R }2$ $182 \div 9 = 20\text{ R }2$ $182 \div 10 = 18\text{ R }2$ $182 \div 11 = 16\text{ R }6$ $182 \div 13 = 14$ The only answer choice that divides into $182$ with no remainder is $13$ $ 14$ $13$ $182$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $13$ are contained within the prime factors of $182$ $182 = 2\times7\times13 13 = 13$ Therefore the only factor of $182$ out of our choices is $13$. We can say that $182$ is divisible by $13$.